Question

Use and euclid algorithm to find the HCF of 1445 and 1190 and express it in the form 1445M +1190N

Answer 1

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Answer 2

Answer:

HCF of 1445 and 1190 is 85.

Step-by-step explanation:

Given two numbers 1445 and 1190.

we have to find the HCF by euclid's algorithm.

By Euclid algorithm lemma,

Dividend= Divisor(Quotient)+Remainder

1445 = 1190 × 1 + 255 →  (1)

1190 = 255 × 4 + 170   → (2)

255 = 170 × 1 + 85

170 = 85 × 2 + 0

Hence, HCF i.e highest common factor is 85

Now, 85 = 255 - 170 [ from ( 1 ) ]

              = [1445 - (1190 × 1)] - [1190 - (255 × 4)]

              = 1445 - 1190 - 1190 + (255 × 4)

              = 1445 - (2 × 1190) + (1445 - (1190 × 1)) × 4   [ from ( 1 ) ]

              = 1445 - (2 × 1190) + (4 × 1445) - (4 × 1190)

              = 1190 ( - 6 ) + 1445 ( 5 )

Comparing with HCF = 1190m + 1445n

we get, m = - 6 and n = 5

Hence, HCF=1190(-6)+1445(5)